Question

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

Answer 1

$<b><i>$

Let O be center, OP be radius.

Applying Pythagoras

PQ = 24, OQ = 25

OQ^2 = OP^2 + PQ^2

25^2 = OP^2 + 24^2

625 = OP^2 + 576

OP^2 = 49

OP = 7 cm

Radius of Circle = 7 cm

Answer 2

First, draw a perpendicular from the centre O of the triangle to a point P on the circle which is touching the tangent.

This line will be perpendicular to the tangent of the circle.

So, OP is perpendicular to PQ i.e. OP ⊥ PQ

From the above figure, it is also seen that △OPQ is a right-angled triangle.

It is given that

OQ = 25 cm and PQ = 24 cm

By using Pythagorean theorem in △OPQ,

OQ² = OP² + PQ²

=> (25)² = OP² + (24)²

=> OP² = 625 – 576

=> OP² = 49

=> OP = 7 cm